Nowadays, Internet congestion is indicated by dropping packets when the routers buffers are full, or by dropping packets according to an AQM mechanism such as RED. Many mechanisms have been proposed to eliminate or minimize the effect of packet loss and tackle the consequential inefficiency due the retransmission of the dropped packets. Fast congestion notification (FN), that has been evaluated through simulation and the results have shown an improvement in the average packet delay, reduces the queuing delay and avoids the buffer overflows by controlling the size of instantaneous queue size below the optimal queue size, and control congestion by keeping the average arrival rate close to the outgoing link capacity. Upon arrival of each packet, FN uses the instantaneous queue size and the average arrival rate to compute the packet marking/dropping probability. This paper examines the characteristics of the FN linear packet dropping/marking probability as a function of required/allowed changes in queue level for fixed values of average arrival rate. The paper also studies how changes in the average arrival rate affect the dropping/marking probability function shape.